In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of ``Brownian motors.'' In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cellular molecular machinery: the working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e., nonbiological, nanopores, lithographic tracks, and optical traps, where single-particle currents were first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented here. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noise-assisted shuttling other degrees of freedom such as charge, spin, or even heat and the assembly of chemical synthetic molecular motors. This review ends with a perspective for future pathways and potential new applications.

/pdf/artificial-brownian-motors-controlling-transport-on-the-1553poaezw.pdf

Artificial Brownian motors: Controlling transport on the nanoscale

Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

This paper presents an exercise in comparing the performance of microelectromechanical systems (MEMS) actuators and sensors as a function of operating principle. Data have been obtained from the literature for the mechanical performance characteristics of actuators, force sensors and displacement sensors. On-chip and off-chip actuators and sensors are each sub-grouped into families, classes and members according to their principle of operation. The performance of MEMS sharing common operating principles is compared with each other and with equivalent macroscopic devices. The data are used to construct performance maps showing the capability of existing actuators and sensors in terms of maximum force and displacement capability, resolution and frequency. These can also be used as a preliminary design tool, as shown in a case study on the design of an on-chip tensile test machine for materials in thin-film form.

/pdf/mems-actuators-and-sensors-observations-on-their-performance-1ce9ndvk3j.pdf

MEMS actuators and sensors: observations on their performance and selection for purpose

Sensors based on the detection of small resistance variations are universally recognized as piezoresistive. Being one of the simplest, most common and most investigated classes of sensors, continuous efforts are focused on creating improved devices with higher performance that can be used in many commercial and non–commercial applications (e.g. evaluation of strain, pressure, acceleration, force etc.). Consequently, despite the fact that more than 150 years have passed since the discovery of the piezoresistive effect in some classes of metals and semiconductors, the development of such sensors remains interesting and topical. Moreover, with the advent of second–generation robotics, research on piezoresistive sensors has undergone a massive increase. This paper aims to be a short, self–consistent vademecum which would be useful to researchers and engineers, since it focuses on the fundamentals of theory, materials, and readout–circuit design pertinent to the most recent developments in the field of piezoresistive sensors.

Theory, technology and applications of piezoresistive sensors: A review

Scanning Hall probe microscopy has been used to make a microscopic study of flux structures and dynamics in yttrium barium copper oxide thin-film disks containing a regular $10\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$-period square array of $2.5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$-sized holes (antidots). Images obtained after field cooling the sample to $77\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in very low fields reveal that the holes can trap two flux quanta at this temperature. Scans obtained after zero-field cooling (ZFC) to $77\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and a subsequent applied field cycle clearly display preferential flux channeling along chains of antidots in the direction of maximum induction gradient. Remarkably, upon reversal of field sweep direction, we observe flux ``streaming'' out of the holes towards the sample edges with almost uniform density flux ``stripes'' bridging the holes in the exit direction. We estimate that the antidots can preferentially trap about 15 flux quanta in these ZFC experiments. Classical electrodynamics simulations of our samples appear to be in good qualitative agreement with our results, indicating that many of the observed phenomena may be geometrical effects that depend primarily on the shape and topology of the sample, and potential applications are discussed.

Anisotropic vortex channeling in YBa2Cu3O7-δ thin films with ordered antidot arrays

We report the development of an advanced sensor for atomic force-guided scanning Hall probe microscopy whereby both a high mobility heterostructure Hall effect magnetic sensor and an n-Al0.4Ga0.6As piezoresistive displacement sensor have been integrated in a single III–V semiconductor cantilever. This allows simple operation in high-vacuum/variable-temperature environments and enables very high magnetic and topographic resolution to be achieved simultaneously. Scans of magnetic induction and topography of a number of samples are presented to illustrate the sensor performance at 300 and 77 K.

/pdf/integrated-piezoresistive-sensors-for-atomic-force-guided-396si0pvz2.pdf

Integrated piezoresistive sensors for atomic force-guided scanning Hall probe microscopy

In this paper we report the development of a new III–V cantilever-based atomic force sensor with piezoresistive detection and an integrated Hall probe for scanning Hall probe microscopy. We give detailed descriptions of the fabrication process and characterization of the new integrated sensor, which will allow the investigation of magnetic samples with no sample preparation at both room and cryogenic temperatures. We also introduce a novel piezoresistive material based on the ternary alloy n+-Al0.4Ga0.6As which allows us to achieve a cantilever deflection sensitivity ΔR/(R Δz) = 2 × 10−6 A−1 at room temperature.

/pdf/micromachined-iii-v-cantilevers-for-afm-tracking-scanning-210abnrkcn.pdf

S. J. Bending

Papers

Anisotropic vortex channeling in YBa2Cu3O7-δ thin films with ordered antidot arrays

Integrated piezoresistive sensors for atomic force-guided scanning Hall probe microscopy

Micromachined III-V cantilevers for AFM-tracking scanning Hall probe microscopy

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Scanning Hall probe microscopy of ferromagnetic structures